论文标题
具有非双向收缩指数的矩阵模型的数值和分析研究
Numerical and analytical studies of a matrix model with non-pairwise contracted indices
论文作者
论文摘要
在汉密尔顿形式主义中是张量模型的规范张量模型，可以直接量化并具有精确的物理状态。该状态通过具有通风函数的广义形式的波函数表示。最简单的状态可观察到的可以通过包含非对索引收缩的矩阵模型表示。该矩阵模型的形式与旋转眼镜的球形$ p $ spin模型应用于副本$ p $ spin模型时出现的形式相同，但是我们的情况具有不同的变量和旋转玻璃盒的参数范围。我们通过分析和数值分析矩阵模型。我们在规范张量模型的一致性条件下所需的位置显示了连续相变的存在的证据。我们还表明，在过渡区域周围存在配置的尺寸过渡。讨论了结果对规范张量模型的含义。
The canonical tensor model, which is a tensor model in the Hamilton formalism, can be straightforwardly quantized and has an exactly solved physical state. The state is expressed by a wave function with a generalized form of the Airy function. The simplest observable on the state can be expressed by a matrix model which contains non-pairwise index contractions. This matrix model has the same form as the one that appears when the replica trick is applied to the spherical $p$-spin model for spin glasses, but our case has different ranges of variables and parameters from the spin glass case. We analyze the matrix model analytically and numerically. We show some evidences for the presence of a continuous phase transition at the location required by a consistency condition of the canonical tensor model. We also show that there are dimensional transitions of configurations around the transition region. Implications of the results to the canonical tensor model are discussed.
